Part II of the Tri-Parametric Information Synthesis (TPIS) Framework. Sequel to: Tri-Parametric Information Synthesis. Abstract: Current cosmological models struggle to provide a first-principles derivation for the observed tight correlation between the mass of supermassive black holes and the velocity dispersion of their host galaxies (the M-sigma relation). Furthermore, the classical description of black holes necessitates a singularity, which violates the principles of discrete information storage. Building upon the Tri-Parametric Information Synthesis (TPIS), which successfully derived the galactic acceleration scale aₜh ≈ cH0/2π from entropic principles, this paper extends the framework to the regime of strong gravity. We propose that the event horizon represents a saturation of information density, governed by the same critical acceleration threshold aₜh that dictates galactic dynamics. By equating the entropic acceleration at the black hole's sphere of influence to the cosmic information limit, we analytically derive the M ∝ σ⁴ scaling relation without invoking feedback mechanisms. Additionally, we argue that the quantization of spacetime at the horizon prevents the formation of a singularity, suggesting black holes are stable, maximum-entropy states of spacetime storage. This "Crystallization" mechanism provides a physical basis for the "Firewall" phenomenon and resolves the Information Paradox. The model is empirically validated against the Magorrian relation (deriving the mass ratio ξ² ≈ 0. 16%) and offers a precise, falsifiable prediction for Gravitational Wave Echoes (e. g. , Δt ≈ 0. 273s for GW150914), which aligns with tentative detections in LIGO data.
Thomas van Walstijn (2026) studied this question.